The generalized point-vortex problem and rotating solutions to the Gross–Pitaevskii equation on surfaces of revolution

We study the generalized point-vortex problem and the Gross–Pitaevskii equation on a surface of revolution. We find rotating periodic solutions to the generalized point-vortex problem, which have two rings of nn equally spaced vortices with degrees ±1. In particular we prove the existence of such solutions when the surface is longitudinally symmetric. Then we seek a rotating solution to the Gross–Pitaevskii equation having vortices that follow those of the point-vortex flow for εε sufficiently small.